Here is a quick glance of airports in Taiwan with domestic flights.
There are three main airlines for domestic flights to choose from — Mandarin Airlines, UNI Air and Daily Air. Mandarin Airlines is the domestic airline subsidiary of China Airlines. Uni Air is the domestic airline subsidiary of EVA Airways. Daily Air is a private airline company that mostly services passengers traveling to the outlying islands from Taitung.
On the Mandarin Airlines website, there is an English version if you check the top right corner. To look for domestic flights, you would want to click the circled option in the image below.
Here is also an english version of the booking page. If you are using the mandarin site, something like this (↓) should appear.
The last column on the right has different options. The one in red indicates that the tickets are either sold out or are not on sale yet. Click the blue button if you want to purchase the ticket. Once you click the blue bottom, this (↓) should pop up. Below is the mandarin and the english version.
You then fill out your personal information in the next step. The Mandarin and English version are both presented below.
It should bring you to this (↓) travel insurance page.
The UNI Air website also has a variety of options for domestic flights. There is an English version of the website (the top right corner). If you are looking for a trip around Taiwan that includes multiple cities, please click on the multi-city button then start planning your trip.
Daily Air only provides information in Mandarin, here is a quick and easy guide.
*Disclaimer: In order to protect the rights and interests of outlying island residents, the number of tickets purchased online for each flight is only open (inclusive) 4 places.*
*If you choose round trip there will be another line right underneath the departure date that says 回程日期, which means return date*
If you are booking a round trip, the first table is for your departure flight date and the second table (right below) is for your return flight date. You should select one of each then move on to the next page.
After you click the 選取 button, scroll down till the table ends and click on the button that says 確認送出 (confirm). This should take you to the next page to fill out your personal information. Please fill out everything on the form as indicated above the table (the red box).
Below is the dropdown list of the type of tickets that are available and the types of ID you could use.